Born in Chicago, Illinois, Fleck moved to Santa Barbara, California with his family in 1957. A student of theater from Santa Barbara City College, he found his theatrical singing voice with lead roles in musicals such as, The King and I and Carousel. Jerry later received his BA degree in Theater Arts from Cal State Long Beach, where he also held lead roles in theatrical productions. He also graduated from the American Academy of Dramatic Art in New York City. He began his professional career as an actor in dinner theater productions, rather than as an assistant director. He first appeared in the 1977 drama The Lincoln Conspiracy, co-starring John Anderson and Whit Bissell and directed by James L. Conway. The following year, he was Conway's First Assistant Director for the 1978 documentary Beyond and Back. Fleck also had a featured part in the 1981 science fiction comedy Earthbound, also directed by Conway.

Afterward, Fleck became a First Assistant Director on the hit action television series Hunter, A-Team, and MacGyver. He was also Second Assistant Director for the 1988 horror comedy Beetlejuice and First Assistant Director for 1990's Edward Scissorhands, both for director Tim Burton. Other credits as first assistant director include Conway's war drama Last of the Mohicans (1977), the television drama Fire in the Dark (1991), and the science fiction thriller Running Delilah (1993, starring Kim Cattrall). As second assistant director he worked on the television comedy The Nashville Grab (1981), the drama Body Rock (1984), the television series Hardcastle and McCormick (1985, starring Brian Keith and Daniel Hugh Kelly), the television western Desperado (1987), and the horror sequel Halloween 4: The Return of Michael Myers (1988, with George P. Wilbur).

He became a part of the Star Trek legacy in 1992 when he became First Assistant Director on Star Trek: The Next Generation, replacing Brad Yacobian, who was promoted to Unit Production Manager. He stayed with the show until its end in 1994. Afterward, Fleck served as First Assistant Director for all seven seasons of Star Trek: Voyager, as well as Star Trek: First Contact and Star Trek: Insurrection.

After Voyager ended its run in 2001, Fleck became First Assistant Director on Star Trek: Enterprise. He was serving in this capacity when, during the show's third season in September of 2003, he died suddenly in his sleep at the age of 55 in Saugus, California. Production was shut down on the set of Enterprise for an entire day as the cast and crew learned of his passing. He had been a part of the Star Trek franchise for eleven years. The third season Enterprise episode "Extinction" was dedicated to his memory.